(*
copyright (c) 2013-2014, simon cruanes
all rights reserved.

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modification, are permitted provided that the following conditions are met:

redistributions of source code must retain the above copyright notice, this
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form must reproduce the above copyright notice, this list of conditions and the
following disclaimer in the documentation and/or other materials provided with
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*)

(** {1 Functional Circular List}

Those are infinite lists that are built from a finite list of
elements, and cycles through them. *)

type 'a t = {
  front : 'a list;
  f_len : int;
  rear : 'a list;
  r_len : int;
}
(* invariant: if front=[] then rear=[] *)

let make f f_len r r_len = match f with
  | [] ->
      assert (f_len = 0);
      { front=List.rev r; f_len=r_len; rear=[]; r_len=0; }
  | _::_ -> {front=f; f_len; rear=r; r_len; }

let singleton x = make [x] 1 [] 0

let of_list l =
  if l = [] then raise (Invalid_argument "empty list");
  make l (List.length l) [] 0

let length l = l.f_len + l.r_len

(*$Q
  (Q.list Q.small_int) (fun l -> \
    l = [] || \
    let q = of_list l in \
    let _, q = next q in \
    length q = List.length l)
*)

let cons x l = make (x::l.front) (l.f_len+1) l.rear l.r_len

let snoc l x = make l.front l.f_len (x::l.rear) (l.r_len+1)

let next l = match l.front with
  | [] -> assert false
  | x::l' ->
      x, make l' (l.f_len-1) (x::l.rear) (l.r_len+1)

let rev l = make l.rear l.r_len l.front l.f_len

let find p l =
  let rec _find p i l =
    if i = 0 then None
    else
      let x, l' = next l in
      if p x then Some x else _find p (i-1) l'
  in
  _find p (length l) l

let mem ?(eq=fun x y -> x=y) x l =
  match find (eq x) l with
  | None -> false
  | Some _ -> true

let exists p l = match find p l with
  | None -> false
  | Some _ -> true

(*$T
 exists (fun x-> x mod 2 = 0) (of_list [1;3;5;7;8])
 not (exists (fun x-> x mod 2 = 0) (of_list [1;3;5;7;9]))
 *)

let for_all p l =
  let rec _check i l =
    i = 0 ||
    ( let x, l' = next l in
      p x && _check (i-1) l')
  in
  _check (length l) l

let fold f acc l =
  let rec _fold acc i l =
    if i=0 then acc
    else
      let x, l' = next l in
      let acc = f acc x in
      _fold acc (i-1) l'
  in
  _fold acc (length l) l

type 'a gen = unit -> 'a option
type 'a sequence = ('a -> unit) -> unit

let gen l =
  let l = ref l in
  fun () ->
    let x, l' = next !l in
    l := l';
    Some x

(*$Q
  (Q.list Q.small_int) (fun l -> \
    l = [] || let q = of_list l in \
    gen q |> CCGen.take (List.length l) |> CCGen.to_list = l)
  *)

let seq l k =
  let r' = lazy (List.rev l.rear) in
  while true do
    List.iter k l.front;
    List.iter k (Lazy.force r')
  done